There's a play area with water ( I've seen it change from CuriousGeorge to SpongeBob to Grinch - not sure what it is now ).
The 7 year old might love the Simpsons - not sure of the height rqmt, but it's the best ride there.
There's a funny 4D Shrek movie.
Most of the other stuff may not suit kids that young - effects show maybe, but probably not that interested in the tram tour and definitely not the Mummy or Jurassic park unless they're really brave - or the monster show or Terminator.
Even with everything Universal isn't a full day for an adult in my opinion. Long trip for little payoff....not at all like the one in Orlando.
We had ap's for a year on a buy a day deal - went 4 times or so with a 13 year old, but no urge to renew.